Invariable or less variable values of a continuous physical quantity in a long time is called as a steady state process; and the transition between two steady state processes within a short time is called as a transient state process. The physical quantity of a process which consists of the steady state process and the transient state process is sampled according to the Nyquist's sampling theorem (also known as the Shannon's theorem), and the sampling time intervals are less than a half of a minimum time constant Tc in the transient state process. There would be too more data to be transmitted in remote automations, if the data were sampled according to the sampling theorem.
In practice, a sampling time interval T is artificially specified in remote automations, and only the data which are on time points of integral multiple of the interval T are recorded or transmitted as shown in FIG. 1. Obviously, the T can not meet the sampling theorem, so that the aliasing is generated, the state and the variability of a physical process can not be correctly reflected by the recorded or transmitted data.
Even if the measured data are replaced by mean values within the time interval T, the fault of the sampled data can not be solved with aliasing generated, but also extra errors will be generated, so that a product relationship no longer exists in the mean value of three quantities in which the product is originally equal to the product of two quantities, e.g. the variable quantities A, B and C, wherein A=B·C, B= B+Δb, C= C+Δc, Ā≠ B· C.